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Calculate the number of molecules in a sample ofan ideal gas whose volume is 0.45 L at 67°C and0.76 bar pressure. |
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Answer» Answer: Explanation:
→ First convert the temperature from °C to K 67° C = 67 + 273.15 = 340.15 K → Now convert the pressure from bar to atm 0.76 bar = 0.75 atm → Now we have to find the number of moles of gas → By ideal gas equation we know that, PV = n R T where R is the gas constant and the value of R = 0.0821 L atm mol⁻¹ K⁻¹ → Substitute the given datas 0.75 atm × 0.45 L = n × 0.0821 L atm mol⁻¹ K⁻¹ × 340.15 K n = (0.3375/27.926) mol n = 0.012 mol → Hence the number of moles of gas is 0.012 moles. → Now the number of molecules of gas is given by Number of molecules of gas = number of moles × Avogadro's number where Avogadro's number = 6.022 × 10²³ → SUBSTITUTING the VALUES, Number of molecules = 0.012 × 6.022 × 10 ²³ Number of molecules = 0.072 × 10²³ Number of molecules = 7.2 × 10²¹ molecules → The ideal gas equation is given by PV = n R T where P is the pressure, V = volume, n = number of moles, R = gas constant, T = temperature
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